Principles of the Magnetic Methods in Geophysics

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• Publisher: Elsevier Science
• Year: 2008
• ISBN:
  9780080931852
• Topic: Physical Sciences
• Subtopic: Geophysics

Magnetic methods are widely used in exploration, engineering, borehole and global geophysics, and the subjects of this book are the physical and mathematical principles of these methods regardless of the area of application.
Beginning with Ampere's law, the force of interaction between currents is analyzed, and then the concept of the magnetic field is introduced and the fundamental features are discussed.
Special attention is paid to measurements of relaxation processes, including topics as the spin echoes or refocusing. Also the special role of the magnetic method in the development of the plate tectonic theory is described.* covers all the physical and mathematical principles of magnetic methods regardless of the area of application.
* presents thorough developments of magnetic methods.

Chapter 1 Magnetic Field in a Nonmagnetic Medium

Alex A. Kaufman, Richard O. Hansen, Robert L.K. Kleinberg

Abstract
Publisher Summary

This chapter focuses on the magnetic field in a nonmagnetic medium. Numerous experiments performed at the beginning of the19th century demonstrated that constant currents interact with each other that mean mechanical forces act at every element of the circuit. Certainly, this is one of the amazing phenomena of the nature and would have been very difficult to predict. In fact, it is almost impossible to expect that the motion of electrons inside of wire may cause a force on moving charges somewhere else, for instance, in another wire with current, and for this reason the phenomenon of this interaction was discovered by chance. By analogy with the attraction field caused by masses, it is proper to assume that constant (time-invariant) currents create a field and because of the existence of this field and of the existence of this field, other current elements experience the action of the force F. Such a field is called the magnetic field, and it can be introduced from Ampere’s law.

1.1 Interaction of constant currents and Ampere's law

Numerous experiments performed at the beginning of the19th century demonstrated that constant currents interact with each other; that is mechanical forces act at every element of the circuit. Certainly, this is one of the amazing phenomena of the nature and would have been very difficult to predict. In fact, it is almost impossible to expect that the motion of electrons inside of wire may cause a force on moving charges somewhere else, for instance, in another wire with current, and for this reason the phenomenon of this interaction was discovered by chance. It turns out that this force of interaction between currents in two circuits depends on the magnitude of these currents, the direction of charge movement, the shape and dimensions of circuits, as well as the their mutual position with respect to each other. The list of factors clearly shows that the mathematical formulation of the interaction of currents should be much more complicated task than that for masses or electric charges. In spite of this fact, Ampere was able to find a relatively simple expression for the force of the interaction of so-called elementary currents:

(1.1)

where I₁ and I₂ are magnitudes of the currents in the linear elements dl(p) and dl(q), respectively, and their direction coincides with that of the current density; L_qp the distance between these elements and is directed from the point q to the point p, which can be located at the center of these elements; finally μ₀ is a constant equal to

and is often called the magnetic permeability of free space. Certainly, this is confusing definition, since free space does not have any magnetic properties. We will use the S.I. system of units where the distance is measured in meters and force in newtons. Of course, with a change of the system...

Table of contents

• Cover image
• Title page
• Table of Contents
• Copyright page
• Dedication
• Introduction
• Acknowledgments
• List of Symbols
• Chapter 1: Magnetic Field in a Nonmagnetic Medium
• Chapter 2: Magnetic Field Caused by Magnetization Currents
• Chapter 3: Magnetic Field in the Presence of Magnetic Medium
• Chapter 4: Main Magnetic Field of the Earth
• Chapter 5: Uniqueness and the Solution of the Forward and Inverse Problems
• Chapter 6: Paramagnetism, Diamagnetism, and Ferromagnetism
• Chapter 7: Nuclear Magnetism Resonance and Measurements of Magnetic Field
• Bibliography
• Appendix
• Subject Index